Analysis And Verification Of QCM Mass Sensitivity

QCM(Quartz Crystal Microbalance)occurs in 1960 s as a micro-mass measurement device based on piezoelectric effect.Because of its nanogram-level detection ability,simple structure,low detection cost and real-time monitoring,it is widely used in biochemistry,food safety,environmental protection etc.However,one needs to know the linear relationship between loading mass and resonace frequency offset before taking it into practical use,which limits the use of QCM.In addition,the electrodes on the surface influence the forced vibration.So each region has different displacement which is caused by inverse piezoelectric effect.That leads to uneven distribution of the mass sensitivity,which makes low repeatability and large measurement error while using QCM in application.These disadvantages hinder the popularization of QCM.Based on the piezoelectric characteristics and vibration characteristics of quartz crystal,the calculation method of QCM's mass sensitivity is deduced and the factors influencing QCM's mass sensitivity are analyzed.The main contents of this paper are:First,we introduce the characteristics of quartz crystal,the piezoelectric effect,frequency-temperature characteristic and quartz crystal resonator equivalent circuit.Second,based on the piezoelectric equation and the particle displacement equation of quartz crystal,we deduce the vibration amplitude of the quartz crystal resonator in different area,and then obtain the method of calculating the mass sensitivity.We use Matlab to analyze the distribution of the QCM's mass sensitivity,and the result shows that the mass sensitivity has max value at the center of the electrode and exponentially decaying away from the center.Then we use Matlab as simulation tool to analyze the influence of electrode thickness,electrode size,quartz wafer thickness and the electrode density on the mass sensitivity,which can provide theoretical reference while designing a QCM.Due to the effect of energy trap,the QCM's non-electrode area is larger than the electrode area.So the non-electrode region cannot be neglected while using in mass measurement.Therefore,we analyze the influence of the non-electrode region on mass measurement.Third,in the liquid phase the resonant frequency offset has relationships with liquid's viscoelasticity,so if we known the viscosity and density of the liquid,the theoretical resonant frequency offset can be calculated.Then we use water and organic reagents as the measured object,and we mearsue the frequency shift of QCM and compare it with the theoretical frequency shift.The maximum relative error between the measured value and the theoretical value is not more than 8.2%.